A=[10.25;01];

B=[0.0063;0.0500];

C=[10];

D=0;

U=[00;00];

setlmis([])

P=lmivar(1,[21]);

Q=lmivar(1,[21]);

R=lmivar(1,[21]);

S=lmivar(1,[21]);

M=lmivar(1,[21]);

N=lmivar(1,[21]);

K=lmivar(2,[12]);

F=lmivar(2,[21]);

lmiterm([111S],1,1);

lmiterm([111P],-1,1);

lmiterm([1510],A);

lmiterm([151K],B,1);

lmiterm([161F],-1,C);

lmiterm([122S],-1,1);

lmiterm([162F],1,C);

lmiterm([133R],1,1);

lmiterm([133Q],-1,1);

lmiterm([153K],B,-1);

lmiterm([163F],1,C);

lmiterm([1630],-A);

lmiterm([144R],-1,1);

lmiterm([155M],-1,1);

lmiterm([166N],-1,1);

lmiterm([-211P],1,1);

lmiterm([-2210],1);

lmiterm([-222M],1,1);

lmiterm([-311Q],1,1);

lmiterm([-3210],1);

lmiterm([-322N],1,1);

lmiterm([-411P],1,1);

lmiterm([-511Q],1,1);

lmiterm([-611R],1,1);

lmiterm([-711S],1,1);

lmiterm([-811M],1,1);

lmiterm([-911N],1,1);

lmisys=getlmis;

[tmin,xfeasp]=feasp(lmisys)

PP=dec2mat(lmisys,xfeasp,P)

QQ=dec2mat(lmisys,xfeasp,Q)

RR=dec2mat(lmisys,xfeasp,R)

SS=dec2mat(lmisys,xfeasp,S)

MM=dec2mat(lmisys,xfeasp,M)

NN=dec2mat(lmisys,xfeasp,N)

KK=dec2mat(lmisys,xfeasp,K)

FF=dec2mat(lmisys,xfeasp,F)

fori=1:100

n=decnbr(lmisys);

c=zeros(n,1);

forj=1:n

[Pj,Qj,Rj,Sj,Mj,Nj,Kj,Fj]=defcx(lmisys,j,P,Q,R,S,M,N,K,F);

c(j)=trace(PP*Mj+MM*Pj+QQ*Nj+NN*Qj);

end

options=[1e-4,0,0,0,0];

[copt,xopt]=mincx(lmisys,c,options)

PPP=dec2mat(lmisys,xopt,P);

QQQ=dec2mat(lmisys,xopt,Q);

RRR=dec2mat(lmisys,xopt,R);

SSS=dec2mat(lmisys,xopt,S);

MMM=dec2mat(lmisys,xopt,M);

NNN=dec2mat(lmisys,xopt,N);

KKK=dec2mat(lmisys,xopt,K);

FFF=dec2mat(lmisys,xopt,F);

Z=[SSS-PPP,U,U,U,(A+B*KKK)',-(FFF*C)';

U,-SSS,U,U,U,(FFF*C)';

U,U,RRR-QQQ,U,-(B*KKK)',-(A-FFF*C)';

U,U,U,-RRR,U,U;

A+B*KKK,U,-B*KKK,U,-inv(PPP),U;

-FFF*C,FFF*C,-(A-FFF*C),U,U,-inv(QQQ)];

Y=eig(Z);

i2=0;

fori1=1:length(Y),

if(Y(i1,1)<0),

i2=i2+1;

end

end

if(i2==length(Y)),

break;

end

PP=PPP

QQ=QQQ

RR=RRR

SS=SSS

MM=MMM

NN=NNN

KK=KKK

FF=FFF

end

if(i==10),

disp('Thereisnoresult');

end

SolverforlinearobjectiveminimizationunderLMIconstraints

Iterations:Bestobjectivevaluesofar

149.439545

236.063874

323.102877

414.567845

514.567845

613.442476

***newlowerbound:0.296420

713.442476

***newlowerbound:1.679189

812.669593

***newlowerbound:3.515934

912.669593

***newlowerbound:4.285731

1011.916238

***newlowerbound:4.395605

1111.916238

***newlowerbound:5.063925

129.631247

***newlowerbound:5.242941

139.178411

***newlowerbound:5.879022

148.769358

***newlowerbound:6.390317

158.502939

***newlowerbound:6.790746

168.326950

***newlowerbound:7.100688

178.238591

***newlowerbound:7.338510

188.176522

***newlowerbound:7.520225

198.161872

***newlowerbound:7.658027

208.161872

***newlowerbound:7.790606

218.147783

***newlowerbound:8.066778

228.114291

238.106330

***newlowerbound:8.074037

248.104751

***newlowerbound:8.080386

258.104153

***newlowerbound:8.085205

268.103217

***newlowerbound:8.089119

278.102513

***newlowerbound:8.091864

288.101985

***newlowerbound:8.093950

298.101589

***newlowerbound:8.095533

308.101291

***newlowerbound:8.096731

318.101177

***newlowerbound:8.097637

328.100996

***newlowerbound:8.098334

338.100859

***newlowerbound:8.098850

348.100806

***newlowerbound:8.099240

358.100721

***newlowerbound:8.099951

Result:feasiblesolutionofrequiredaccuracy

bestobjectivevalue:8.100721

guaranteedrelativeaccuracy:9.50e-05

f-radiussaturation:0.000%ofR=1.00e+09

copt=

8.1007

xopt=

0.1639

0.0030

1.3573

0.3663

1.0277

18.7011

0.0038

-0.0173

0.0812

0.0001

-0.0007

0.0061

6.1002

-0.0135

0.7368

3.2584

-0.1709

0.0646

-0.5553

-2.7823

0.0001

-0.0000

PP=

0.16390.0030

0.00301.3573

QQ=

0.36631